The Poincaré algebra is spanned on the two physical degrees of freedom which we call \(h(x)\)  with helicity 2 and \(\bar{h}(x)\)  with helicity \(-2\) . We have chosen \(x^+\)  as the evolution parameter, “time” according to Dirac's prescription [1]}. One of the Poincaré generators, the conjugate momentum \(P_+\) , is the light-cone Hamiltonian. The light-cone Poincaré generators split into two kinds: the kinematical ones (\(\mathbb {K}\) ) which do not involve the time derivative \(\partial _{+}\)  and the dynamical ones that involve time derivatives and hence get non-linear contributions in the interacting theory [2]}. Accordingly, we have the generators (the missing indices refer to the transverse direction as in (REF ))
\(&&\mathbb {K}:\quad \lbrace P, \bar{P}, P_-, J, J^+, \bar{J}^+, J^{+-}\rbrace \,, \nonumber \\&& \mathbb {D}:\quad \lbrace P_+\equiv H, J^-, \bar{J}^-\rbrace \,.\) 
